# 10 Most Common ISEE Upper-Level Math Questions

Preparing for the ISEE Upper-Level Math test? Want a preview of the most common mathematics questions on the ISEE Upper-Level Math test? If so, then you are in the right place.

The mathematics section of ISEE Upper Level can be a challenging area for many test-takers, but with enough patience, it can be easy and even enjoyable!

Preparing for the ISEE Upper-Level Math test can be a nerve-wracking experience. Learning more about what you’re going to see when you take the ISEE Upper Level can help to reduce those pre-test jitters. Here’s your chance to review the 10 most common ISEE Upper-Level Math questions to help you know what to expect and what to practice most. Try these 10 most common ISEE Upper-Level Math questions to hone your mathematical skills and to see if your math skills are up to date on what’s being asked on the exam or if you still need more practice.

Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

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**10 Sample ISEE Upper Level** **Math Practice Questions**

1- Emily and Daniel have taken the same number of photos on their school trip. Emily has taken 5 times as many photos as Claire and Daniel has taken 16 more photos than Claire. How many photos has Claire taken?

A. 4

B. 6

C. 8

D. 10

2- Emily lives 5 \(\frac{1}{4}\) miles from where she works. When traveling to work, she walks to a bus stop \(\frac{1}{3}\) of the way to catch a bus. How many miles away from her house is the bus stop?

A. \(4\frac{1}{3}\) miles

B. \(4\frac{3}{4}\) miles

C. \(2\frac{3}{4}\) miles

D. \(1\frac{3}{4}\) miles

3- Use the diagram below to answer the question.

Given the lengths of the base and diagonal of the rectangle above, what is the length of height h, in terms of s?

A. 2s \(\sqrt{6}\)

B. s \(\sqrt{7}\)

C. 5s

D. 5s\(^2\)

4-

There are also purple marbles in the bag. Which of the following can NOT be the probability of randomly selecting a purple marble from the bag?

A. \(\frac{1}{10}\)

B. \(\frac{1}{4}\)

C. \(\frac{2}{5}\)

D. \(\frac{7}{15}\)

5- A square measures 6 inches on one side. By how much will the area be increased if its length is increased by 5 inches and its width decreased by 3 inches.

A. 1 sq decreased

B. 3 sq decreased

C. 6 sq decreased

D. 9 sq decreased

6- If a box contains red and blue balls in the ratio of \(2 : 3\) red to blue, how many red balls are there if 90 blue balls are in the box?

A. 40

B. 60

C. 80

D. 30

7- How many \(3 × 3\) squares can fit inside a rectangle with a height of 54 and width of 12?

A. 72

B. 52

C. 62

D. 42

8- David makes a weekly salary of $220 plus \(8\%\) commission on his sales. What will his income be for a week in which he makes sales totaling $1100?

A. $328

B. $318

C. $308

D. $298

9- \(4x^2y^3 + 5x^3y^5 – (5x^2y^3 – 2x^3y^5) = \)

A. \(–x^2y^3\)

B. \(6x^2y^3 – x^3y^5\)

C. \(7x^2y^3\)

D. \(7x^3y^5 – x^2y^3\)

10- If the area of trapezoid is 126 cm, what is the perimeter of the trapezoid?

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## Answers:

1- **A**

Emily = Daniel

Emily = 5 Claire

Daniel = \(16 +\) Claire

Emily = Daniel → Emily = \(16 +\) Claire

Emily = 5 Claire → 5 Claire = \(16 +\) Claire → 5 Claire \(–\) Claire = 16

4 Claire = 16

Claire = 4

2- **D**

\(\frac{1}{3}\) of the distance is \(5\frac{1}{4}\) miles. Then:

\(\frac{1}{3} × 5 \frac{1}{4} = \frac{1}{3} × \frac{21}{4}= \frac{21}{12}\)

Converting \(\frac{21}{12}\) to a mixed number gives:

\(\frac{21}{12}= 1\frac{9}{12}=1\frac{3}{4}\)

3-** A**

Use Pythagorean theorem:

\(a^2+b^2=c^2→s^2+h^2=(5s)^2→s^2+h^2=25s^2\)

Subtracting (s^2) from both sides gives: \( h^2=24s^2\)

Square roots of both sides: \(h=\sqrt{24s^2}=\sqrt{4×6×s^2 } =\sqrt 4 × \sqrt6 × \sqrt{s^2 }=2 × s × \sqrt6 = 2s\sqrt6\)

4- **D**

Let \(x\) be the number of purple marbles. Let’s review the choices provided:

A. \(\frac{1}{10}\), if the probability of choosing a purple marble is one out of ten, then:

\(Probability=\frac{number \space of \space desired \space outcomes}{number \space of \space total \space outcomes}=\frac{x}{20+30+40+x}=\frac{1}{10}\)

Use cross multiplication and solve for x. \(10x=90+x→9x=90→x=9\)

Since, number of purple marbles can be 9, then, choice be the probability of randomly selecting a purple marble from the bag.

Use the same method for other choices.

B. \(\frac{1}{4}\)

\(\frac{x}{20+30+40+x}=\frac{1}{4}→4x=90+x→3x=90→x=30\)

C. \(\frac{2}{5}\)

\(\frac{x}{20+30+40+x}=\frac{2}{5}→5x=180+2x→3x=180→x=60\)

D. \(\frac{7}{15}\)

\(\frac{x}{20+30+40+x}=\frac{7}{15}→15x=630+7x→8x=630→x=78.75\)

Number of purple marbles cannot be a decimal.

5- **B**

The area of the square is 36 square inches.

\(Area of square=side×side=6×6=36\)

The length of the square is increased by 5 inches and its width decreased by 3 inches. Then, its area equals:

Area of \(rectangle=width×length=11×3=33\)

The area of the square will be decreased by 3 square inches.

\(36-33=3\)

6- **B**

Write a proportion and solve.

\(\frac{2}{3}=\frac{x}{90}\)

Use cross multiplication:

\(3x=180→x=60\)

7- **A**

Number of squares equal to: \(\frac{54×12}{3×3} = 18 × 4 = 72\)

8- **C**

David’s weekly salary is $220 plus \(8\%\) of $1,100. Then:

\(8\% \space of \space 1,100=0.08 × 1,100 = 88\)

\(220+88=308\)

9- **D**

\(4x^2y^3 + 5x^3y^5 – (5x^2y^3 – 2x^3y^5) = 4x^2y^3 + 5x^3y^5 – 5x^2y^3 + 2x^3y^5 = – x^2y^3 + 7 x^3y^5\)

10- **13**

The area of the trapezoid is:

\(Area=\frac{1}{2}h(b_1+b_2 )=\frac{1}{2}(x)(13+8)=126\)

\(→10.5x=126→x=12\)

\(y=\sqrt{5^2 +12^2 } = \sqrt{25+144} = \sqrt{169} = 13\)

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